When \(\phi (t)=(1-\lambda )(t)_+^p+\lambda (t)_-^p\) , where \(p>1\) , \(\lambda \in [0,1]\) , \((t)_+:=\max \lbrace t,0\rbrace \)  and \((t)_-:=\max \lbrace -t,0\rbrace \) , the affine Orlicz Pólya-Szegö principle becomes the general affine Pólya-Szegö-type principle (established in [1]}). The symmetric affine Pólya-Szegö principle [2]} and the asymmetric affine Pólya-Szegö principle [3]} correspond to the cases of \(\lambda =1/2\)  and \(\lambda =0\) , respectively.
